This protocol will determine the antihemostatic dose-response effects of HIRULOG(TM) in renal failure patients treated with chronic hemodialysis by administering the drug according to a dose escalating regimen while measuring platelet and coagulation hemostatic functions. This study will document a safe and effective regimen for use in testing the hypothesis that this direct antithrombin peptide prevents failure of arteriovenous (AV) vascular access grafts in dialysis patients.